Details

analyze11.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
37.5%	37.5%	25.1%	2
37.5%	18.7%	43.8%	3
46.8%	9.4%	43.8%	4
51.5%	4.7%	43.8%	5
51.5%	2.3%	46.1%	6
52.7%	1.2%	46.1%	7
53.3%	0.6%	46.1%	8
53.3%	0.3%	46.4%	9
53.4%	0.1%	46.4%	10
53.5%	0.1%	46.4%	11
53.5%	0%	46.5%	12
53.5%	0%	46.5%	13
53.5%	0%	46.5%	14

Compiler

Compiled 70 to 33 computations (52.9% saved)

sample45.0ms (0.2%)

Algorithm

1×

intervals

Results

28.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 137 to 65 computations (52.6% saved)

simplify215.0ms (1%)

Algorithm

1×	egg-herbie

Rules

744×	`distribute-lft-out_binary64_1734`
629×	`associate-/l/_binary64_1730`
586×	`associate-/l*_binary64_1728`
496×	`associate-/r*_binary64_1727`
430×	`distribute-rgt-in_binary64_1733`
425×	`*-commutative_binary64_1714`
381×	`unswap-sqr_binary64_1751`
332×	`distribute-rgt-out_binary64_1736`
281×	`associate-+l+_binary64_1716`
273×	`associate-*r/_binary64_1725`
213×	`associate-*l/_binary64_1726`
183×	`*-lft-identity_binary64_1772`
179×	`associate-l_binary64_1724`
165×	`distribute-lft-in_binary64_1732`
157×	`associate-r_binary64_1723`
133×	`*-rgt-identity_binary64_1773`
126×	`sqr-pow_binary64_1755`
109×	`+-commutative_binary64_1713`
105×	`associate-+r+_binary64_1715`
68×	`associate-/r/_binary64_1729`
32×	`pow-sqr_binary64_1756`
21×	`cube-prod_binary64_1811`
20×	`pow-plus_binary64_1846`
11×	`unpow3_binary64_1849`
9×	`cube-unmult_binary64_1820`
8×	`cube-mult_binary64_1813`
6×	`/-rgt-identity_binary64_1774`
4×	`unpow2_binary64_1848`
3×	`unpow1_binary64_1841`
2×	`unpow1/2_binary64_1847` `rem-sqrt-square_binary64_1796`
1×	`1-exp_binary64_1827` `sqr-abs_binary64_1798`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_2046` `erf-erfc_binary64_2045` `erf-odd_binary64_2044` `if-if-and-not_binary64_2043` `if-if-and_binary64_2042` `if-if-or-not_binary64_2041` `if-if-or_binary64_2040` `if-not_binary64_2039` `if-same_binary64_2038` `if-false_binary64_2037` `if-true_binary64_2036` `not-gte_binary64_2035` `not-lte_binary64_2034` `not-gt_binary64_2033` `not-lt_binary64_2032` `gte-same_binary64_2031` `lte-same_binary64_2030` `gt-same_binary64_2029` `lt-same_binary64_2028` `sinh---cosh_binary64_1975` `sinh-+-cosh_binary64_1974` `sinh-cosh_binary64_1973` `tanh-def-c_binary64_1972` `tanh-def-b_binary64_1971` `tanh-def-a_binary64_1970` `cosh-def_binary64_1969` `sinh-def_binary64_1968` `tan-neg_binary64_1915` `cos-neg_binary64_1914` `sin-neg_binary64_1913` `tan-0_binary64_1912` `cos-0_binary64_1911` `sin-0_binary64_1910` `hang-m-tan_binary64_1909` `hang-p-tan_binary64_1908` `hang-m0-tan_binary64_1907` `hang-p0-tan_binary64_1906` `hang-0m-tan_binary64_1905` `hang-0p-tan_binary64_1904` `tan-+PI/2_binary64_1903` `tan-+PI_binary64_1902` `tan-PI_binary64_1901` `tan-PI/3_binary64_1900` `tan-PI/4_binary64_1899` `tan-PI/6_binary64_1898` `cos-+PI/2_binary64_1897` `cos-+PI_binary64_1896` `cos-PI_binary64_1895` `cos-PI/2_binary64_1894` `cos-PI/3_binary64_1893` `cos-PI/4_binary64_1892` `cos-PI/6_binary64_1891` `sin-+PI/2_binary64_1890` `sin-+PI_binary64_1889` `sin-PI_binary64_1888` `sin-PI/2_binary64_1887` `sin-PI/3_binary64_1886` `sin-PI/4_binary64_1885` `sin-PI/6_binary64_1884` `sub-1-sin_binary64_1883` `sub-1-cos_binary64_1882` `-1-add-sin_binary64_1881` `-1-add-cos_binary64_1880` `1-sub-sin_binary64_1879` `1-sub-cos_binary64_1878` `cos-sin-sum_binary64_1877` `log-E_binary64_1873` `log-pow_binary64_1872` `log-rec_binary64_1871` `log-div_binary64_1870` `log-prod_binary64_1869` `pow-base-0_binary64_1867` `unpow1/3_binary64_1850` `exp-to-pow_binary64_1845` `pow-base-1_binary64_1843` `unpow0_binary64_1842` `unpow-1_binary64_1840` `exp-lft-cube_binary64_1839` `exp-lft-sqr_binary64_1838` `exp-cbrt_binary64_1837` `exp-sqrt_binary64_1836` `exp-prod_binary64_1835` `div-exp_binary64_1834` `rec-exp_binary64_1833` `prod-exp_binary64_1832` `exp-diff_binary64_1831` `exp-neg_binary64_1830` `exp-sum_binary64_1829` `e-exp-1_binary64_1828` `exp-1-e_binary64_1826` `exp-0_binary64_1825` `rem-log-exp_binary64_1824` `rem-exp-log_binary64_1823` `cube-div_binary64_1812` `cube-neg_binary64_1810` `rem-3cbrt-rft_binary64_1809` `rem-3cbrt-lft_binary64_1808` `rem-cbrt-cube_binary64_1807` `rem-cube-cbrt_binary64_1806` `sqr-neg_binary64_1797` `rem-square-sqrt_binary64_1795` `times-frac_binary64_1789` `div-sub_binary64_1788` `neg-mul-1_binary64_1779` `neg-sub0_binary64_1778` `unsub-neg_binary64_1777` `sub-neg_binary64_1776` `mul-1-neg_binary64_1775` `remove-double-neg_binary64_1771` `sub0-neg_binary64_1770` `--rgt-identity_binary64_1769` `+-rgt-identity_binary64_1768` `+-lft-identity_binary64_1767` `mul0-rgt_binary64_1766` `mul0-lft_binary64_1765` `div0_binary64_1764` `*-inverses_binary64_1763` `+-inverses_binary64_1762` `lft-mult-inverse_binary64_1761` `rgt-mult-inverse_binary64_1760` `remove-double-div_binary64_1759` `difference-of-sqr--1_binary64_1754` `difference-of-sqr-1_binary64_1753` `difference-of-squares_binary64_1752` `swap-sqr_binary64_1750` `cancel-sign-sub-inv_binary64_1749` `cancel-sign-sub_binary64_1748` `distribute-neg-frac_binary64_1747` `distribute-frac-neg_binary64_1746` `distribute-neg-out_binary64_1745` `distribute-neg-in_binary64_1744` `distribute-rgt-neg-out_binary64_1743` `distribute-lft-neg-out_binary64_1742` `distribute-rgt-neg-in_binary64_1741` `distribute-lft-neg-in_binary64_1740` `distribute-rgt1-in_binary64_1739` `distribute-lft1-in_binary64_1738` `distribute-rgt-out--_binary64_1737` `distribute-lft-out--_binary64_1735` `count-2_binary64_1731` `associate--r-_binary64_1722` `associate--l-_binary64_1721` `associate--l+_binary64_1720` `associate--r+_binary64_1719` `associate-+l-_binary64_1718` `associate-+r-_binary64_1717`

Counts

1 → 5

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	77
1	70	62
2	210	45
3	761	41
4	1373	41
5	3002	41
6	3334	41
7	3492	41
8	4100	41
9	4119	41
10	4206	41
11	4850	41
12	5050	41

prune21.0ms (0.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	2	3	5
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	2	4	6

Error

0.0b

Counts

6 → 4

Compiler

Compiled 349 to 198 computations (43.3% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.1b	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
0.2b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0b	(sqrt.f64 PI.f64)

rewrite581.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

41×	`add-sqr-sqrt_binary64_1805`
39×	`add-exp-log_binary64_1821`
38×	`add-cbrt-cube_binary64_1819`
36×	`associate-l_binary64_1724`
35×	`pow1_binary64_1844`
31×	`times-frac_binary64_1789`
29×	`*-un-lft-identity_binary64_1783`
27×	`add-cube-cbrt_binary64_1818`
19×	`prod-exp_binary64_1832`
17×	`cbrt-unprod_binary64_1816`
14×	`sqrt-prod_binary64_1799` `associate-*l/_binary64_1726`
12×	`frac-add_binary64_1791`
10×	`pow-prod-down_binary64_1854`
7×	`associate-r_binary64_1723`
6×	`flip3-+_binary64_1786` `frac-times_binary64_1793` `flip-+_binary64_1757` `unswap-sqr_binary64_1751` `associate-*r/_binary64_1725` `pow-prod-up_binary64_1853` `pow-plus_binary64_1846`
5×	`div-exp_binary64_1834`
4×	`add-log-exp_binary64_1822` `cbrt-undiv_binary64_1817`
3×	`*-commutative_binary64_1714`
2×	`div-inv_binary64_1780` `pow2_binary64_1864` `pow-sqr_binary64_1756`
1×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `1-exp_binary64_1827` `rec-exp_binary64_1833` `distribute-rgt-in_binary64_1733` `distribute-lft-in_binary64_1732` `pow3_binary64_1866` `rem-3cbrt-lft_binary64_1808`

Counts

4 → 140

Calls

4 calls:

28.0ms	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
13.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
6.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
2.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 13127 to 4592 computations (65% saved)

series411.0ms (2%)

Error

0.0b

Counts

4 → 9

Calls

4 calls:

296.0ms	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
56.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
40.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1395 to 766 computations (45.1% saved)

simplify242.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

520×	`associate-r_binary64_1723`
418×	`associate-l_binary64_1724`
389×	`cancel-sign-sub-inv_binary64_1749`
271×	`exp-prod_binary64_1835`
217×	`*-commutative_binary64_1714`
214×	`distribute-rgt-in_binary64_1733`
207×	`unswap-sqr_binary64_1751`
201×	`distribute-lft-in_binary64_1732`
108×	`cube-prod_binary64_1811`
85×	`associate-*l/_binary64_1726`
77×	`swap-sqr_binary64_1750`
67×	`sub-neg_binary64_1776`
65×	`*-rgt-identity_binary64_1773`
64×	`sqr-pow_binary64_1755`
57×	`*-lft-identity_binary64_1772`
54×	`unpow3_binary64_1849` `+-commutative_binary64_1713`
52×	`associate-*r/_binary64_1725`
48×	`associate-/l*_binary64_1728`
46×	`log-prod_binary64_1869`
43×	`associate-+l+_binary64_1716`
39×	`neg-mul-1_binary64_1779`
38×	`neg-sub0_binary64_1778`
33×	`distribute-rgt-neg-in_binary64_1741`
29×	`associate-+r+_binary64_1715`
27×	`distribute-neg-in_binary64_1744` `distribute-lft-neg-in_binary64_1740`
25×	`times-frac_binary64_1789`
21×	`exp-sum_binary64_1829`
20×	`pow-plus_binary64_1846`
19×	`distribute-rgt-neg-out_binary64_1743`
16×	`cube-mult_binary64_1813`
10×	`unsub-neg_binary64_1777` `distribute-rgt-out--_binary64_1737`
9×	`cube-unmult_binary64_1820` `associate--l+_binary64_1720` `associate-+l-_binary64_1718`
8×	`pow-sqr_binary64_1756` `associate-+r-_binary64_1717`
7×	`associate--r+_binary64_1719`
6×	`log-div_binary64_1870` `distribute-lft-neg-out_binary64_1742` `distribute-rgt-out_binary64_1736`
4×	`log-pow_binary64_1872` `rem-sqrt-square_binary64_1796` `/-rgt-identity_binary64_1774` `associate-/r*_binary64_1727`
3×	`difference-of-squares_binary64_1752`
2×	`log-rec_binary64_1871` `unpow1/2_binary64_1847` `cube-div_binary64_1812` `div-sub_binary64_1788` `+-rgt-identity_binary64_1768`
1×	`unpow1/3_binary64_1850` `unpow2_binary64_1848` `exp-lft-sqr_binary64_1838` `1-exp_binary64_1827` `exp-1-e_binary64_1826` `rem-cbrt-cube_binary64_1807` `sqr-abs_binary64_1798` `rem-square-sqrt_binary64_1795` `sub0-neg_binary64_1770` `+-lft-identity_binary64_1767` `count-2_binary64_1731` `associate-/l/_binary64_1730`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_2046` `erf-erfc_binary64_2045` `erf-odd_binary64_2044` `if-if-and-not_binary64_2043` `if-if-and_binary64_2042` `if-if-or-not_binary64_2041` `if-if-or_binary64_2040` `if-not_binary64_2039` `if-same_binary64_2038` `if-false_binary64_2037` `if-true_binary64_2036` `not-gte_binary64_2035` `not-lte_binary64_2034` `not-gt_binary64_2033` `not-lt_binary64_2032` `gte-same_binary64_2031` `lte-same_binary64_2030` `gt-same_binary64_2029` `lt-same_binary64_2028` `sinh---cosh_binary64_1975` `sinh-+-cosh_binary64_1974` `sinh-cosh_binary64_1973` `tanh-def-c_binary64_1972` `tanh-def-b_binary64_1971` `tanh-def-a_binary64_1970` `cosh-def_binary64_1969` `sinh-def_binary64_1968` `tan-neg_binary64_1915` `cos-neg_binary64_1914` `sin-neg_binary64_1913` `tan-0_binary64_1912` `cos-0_binary64_1911` `sin-0_binary64_1910` `hang-m-tan_binary64_1909` `hang-p-tan_binary64_1908` `hang-m0-tan_binary64_1907` `hang-p0-tan_binary64_1906` `hang-0m-tan_binary64_1905` `hang-0p-tan_binary64_1904` `tan-+PI/2_binary64_1903` `tan-+PI_binary64_1902` `tan-PI_binary64_1901` `tan-PI/3_binary64_1900` `tan-PI/4_binary64_1899` `tan-PI/6_binary64_1898` `cos-+PI/2_binary64_1897` `cos-+PI_binary64_1896` `cos-PI_binary64_1895` `cos-PI/2_binary64_1894` `cos-PI/3_binary64_1893` `cos-PI/4_binary64_1892` `cos-PI/6_binary64_1891` `sin-+PI/2_binary64_1890` `sin-+PI_binary64_1889` `sin-PI_binary64_1888` `sin-PI/2_binary64_1887` `sin-PI/3_binary64_1886` `sin-PI/4_binary64_1885` `sin-PI/6_binary64_1884` `sub-1-sin_binary64_1883` `sub-1-cos_binary64_1882` `-1-add-sin_binary64_1881` `-1-add-cos_binary64_1880` `1-sub-sin_binary64_1879` `1-sub-cos_binary64_1878` `cos-sin-sum_binary64_1877` `log-E_binary64_1873` `pow-base-0_binary64_1867` `exp-to-pow_binary64_1845` `pow-base-1_binary64_1843` `unpow0_binary64_1842` `unpow1_binary64_1841` `unpow-1_binary64_1840` `exp-lft-cube_binary64_1839` `exp-cbrt_binary64_1837` `exp-sqrt_binary64_1836` `div-exp_binary64_1834` `rec-exp_binary64_1833` `prod-exp_binary64_1832` `exp-diff_binary64_1831` `exp-neg_binary64_1830` `e-exp-1_binary64_1828` `exp-0_binary64_1825` `rem-log-exp_binary64_1824` `rem-exp-log_binary64_1823` `cube-neg_binary64_1810` `rem-3cbrt-rft_binary64_1809` `rem-3cbrt-lft_binary64_1808` `rem-cube-cbrt_binary64_1806` `sqr-neg_binary64_1797` `mul-1-neg_binary64_1775` `remove-double-neg_binary64_1771` `--rgt-identity_binary64_1769` `mul0-rgt_binary64_1766` `mul0-lft_binary64_1765` `div0_binary64_1764` `*-inverses_binary64_1763` `+-inverses_binary64_1762` `lft-mult-inverse_binary64_1761` `rgt-mult-inverse_binary64_1760` `remove-double-div_binary64_1759` `difference-of-sqr--1_binary64_1754` `difference-of-sqr-1_binary64_1753` `cancel-sign-sub_binary64_1748` `distribute-neg-frac_binary64_1747` `distribute-frac-neg_binary64_1746` `distribute-neg-out_binary64_1745` `distribute-rgt1-in_binary64_1739` `distribute-lft1-in_binary64_1738` `distribute-lft-out--_binary64_1735` `distribute-lft-out_binary64_1734` `associate-/r/_binary64_1729` `associate--r-_binary64_1722` `associate--l-_binary64_1721`

Counts

149 → 478

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	275	6778
1	855	5183
2	3452	4689
3	4818	4623
4	4976	4621
5	4973	4621

prune3.0s (14.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	475	3	478
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	479	3	482

Error

Counts

482 → 3

Compiler

Compiled 40048 to 20111 computations (49.8% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
0.1b	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
0.1b	(.f64 (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 (fabs.f64 x) 2)))) (sqrt.f64 (/.f64 1 PI.f64)))
0.2b	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))

rewrite356.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

49×	`add-sqr-sqrt_binary64_1805`
42×	`associate-r_binary64_1723`
24×	`*-un-lft-identity_binary64_1783`
23×	`add-cube-cbrt_binary64_1818`
21×	`add-exp-log_binary64_1821`
16×	`sqrt-prod_binary64_1799`
14×	`unswap-sqr_binary64_1751`
12×	`add-cbrt-cube_binary64_1819` `unpow-prod-down_binary64_1862` `associate-l_binary64_1724`
11×	`times-frac_binary64_1789`
10×	`prod-exp_binary64_1832`
6×	`pow1_binary64_1844` `sqr-pow_binary64_1755`
4×	`add-log-exp_binary64_1822` `cbrt-unprod_binary64_1816` `cube-prod_binary64_1811` `*-commutative_binary64_1714`
3×	`pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `sqrt-div_binary64_1800`
2×	`flip3-+_binary64_1786` `frac-times_binary64_1793` `flip-+_binary64_1757` `associate-*l/_binary64_1726`
1×	`unpow3_binary64_1849` `cube-mult_binary64_1813` `pow-prod-down_binary64_1854` `associate-*r/_binary64_1725` `div-inv_binary64_1780`

Counts

4 → 120

Calls

4 calls:

25.0ms	(.f64 (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 (fabs.f64 x) 2)))) (sqrt.f64 (/.f64 1 PI.f64)))
7.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
6.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
6.0ms	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))

Compiler

Compiled 5152 to 3682 computations (28.5% saved)

series500.0ms (2.4%)

Error

Counts

4 → 12

Calls

4 calls:

283.0ms	(.f64 (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 (fabs.f64 x) 2)))) (sqrt.f64 (/.f64 1 PI.f64)))
76.0ms	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
65.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
56.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))

Compiler

Compiled 1116 to 867 computations (22.3% saved)

simplify203.0ms (1%)

Algorithm

1×	egg-herbie

Rules

398×	`cancel-sign-sub-inv_binary64_1749`
222×	`distribute-rgt-neg-in_binary64_1741`
197×	`exp-prod_binary64_1835`
192×	`associate-l_binary64_1724`
188×	`log-prod_binary64_1869`
170×	`associate-r_binary64_1723`
158×	`distribute-neg-in_binary64_1744`
154×	`associate-+r+_binary64_1715`
149×	`associate-+l+_binary64_1716`
146×	`sub-neg_binary64_1776`
142×	`sqr-pow_binary64_1755`
109×	`*-commutative_binary64_1714`
107×	`+-commutative_binary64_1713`
102×	`distribute-rgt-in_binary64_1733`
98×	`distribute-lft-in_binary64_1732`
96×	`unsub-neg_binary64_1777`
95×	`neg-mul-1_binary64_1779`
93×	`neg-sub0_binary64_1778`
87×	`cube-prod_binary64_1811`
74×	`unswap-sqr_binary64_1751`
70×	`unpow3_binary64_1849`
68×	`exp-sum_binary64_1829`
67×	`swap-sqr_binary64_1750`
65×	`log-pow_binary64_1872`
62×	`associate--r+_binary64_1719`
51×	`cube-mult_binary64_1813`
43×	`distribute-lft-neg-in_binary64_1740`
42×	`associate--l+_binary64_1720`
29×	`distribute-lft-neg-out_binary64_1742`
28×	`-rgt-identity_binary64_1773` `associate-/l_binary64_1728`
26×	`pow-sqr_binary64_1756`
24×	`*-lft-identity_binary64_1772`
21×	`cube-unmult_binary64_1820` `rem-sqrt-square_binary64_1796`
20×	`pow-plus_binary64_1846` `associate-*r/_binary64_1725`
18×	`associate-*l/_binary64_1726`
14×	`distribute-rgt-neg-out_binary64_1743`
12×	`distribute-rgt-out_binary64_1736`
9×	`times-frac_binary64_1789` `associate-/l/_binary64_1730` `associate-/r*_binary64_1727`
7×	`associate-+l-_binary64_1718` `associate-+r-_binary64_1717`
6×	`+-rgt-identity_binary64_1768` `distribute-rgt-out--_binary64_1737`
5×	`distribute-lft-out_binary64_1734` `associate-/r/_binary64_1729`
3×	`/-rgt-identity_binary64_1774` `sub0-neg_binary64_1770` `difference-of-squares_binary64_1752` `count-2_binary64_1731`
2×	`unpow2_binary64_1848` `unpow1/2_binary64_1847` `rem-square-sqrt_binary64_1795` `associate--l-_binary64_1721`
1×	`unpow1/3_binary64_1850` `exp-lft-sqr_binary64_1838` `prod-exp_binary64_1832` `exp-diff_binary64_1831` `1-exp_binary64_1827` `exp-1-e_binary64_1826` `rem-cbrt-cube_binary64_1807` `rem-cube-cbrt_binary64_1806` `sqr-abs_binary64_1798` `distribute-lft-out--_binary64_1735`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_2046` `erf-erfc_binary64_2045` `erf-odd_binary64_2044` `if-if-and-not_binary64_2043` `if-if-and_binary64_2042` `if-if-or-not_binary64_2041` `if-if-or_binary64_2040` `if-not_binary64_2039` `if-same_binary64_2038` `if-false_binary64_2037` `if-true_binary64_2036` `not-gte_binary64_2035` `not-lte_binary64_2034` `not-gt_binary64_2033` `not-lt_binary64_2032` `gte-same_binary64_2031` `lte-same_binary64_2030` `gt-same_binary64_2029` `lt-same_binary64_2028` `sinh---cosh_binary64_1975` `sinh-+-cosh_binary64_1974` `sinh-cosh_binary64_1973` `tanh-def-c_binary64_1972` `tanh-def-b_binary64_1971` `tanh-def-a_binary64_1970` `cosh-def_binary64_1969` `sinh-def_binary64_1968` `tan-neg_binary64_1915` `cos-neg_binary64_1914` `sin-neg_binary64_1913` `tan-0_binary64_1912` `cos-0_binary64_1911` `sin-0_binary64_1910` `hang-m-tan_binary64_1909` `hang-p-tan_binary64_1908` `hang-m0-tan_binary64_1907` `hang-p0-tan_binary64_1906` `hang-0m-tan_binary64_1905` `hang-0p-tan_binary64_1904` `tan-+PI/2_binary64_1903` `tan-+PI_binary64_1902` `tan-PI_binary64_1901` `tan-PI/3_binary64_1900` `tan-PI/4_binary64_1899` `tan-PI/6_binary64_1898` `cos-+PI/2_binary64_1897` `cos-+PI_binary64_1896` `cos-PI_binary64_1895` `cos-PI/2_binary64_1894` `cos-PI/3_binary64_1893` `cos-PI/4_binary64_1892` `cos-PI/6_binary64_1891` `sin-+PI/2_binary64_1890` `sin-+PI_binary64_1889` `sin-PI_binary64_1888` `sin-PI/2_binary64_1887` `sin-PI/3_binary64_1886` `sin-PI/4_binary64_1885` `sin-PI/6_binary64_1884` `sub-1-sin_binary64_1883` `sub-1-cos_binary64_1882` `-1-add-sin_binary64_1881` `-1-add-cos_binary64_1880` `1-sub-sin_binary64_1879` `1-sub-cos_binary64_1878` `cos-sin-sum_binary64_1877` `log-E_binary64_1873` `log-rec_binary64_1871` `log-div_binary64_1870` `pow-base-0_binary64_1867` `exp-to-pow_binary64_1845` `pow-base-1_binary64_1843` `unpow0_binary64_1842` `unpow1_binary64_1841` `unpow-1_binary64_1840` `exp-lft-cube_binary64_1839` `exp-cbrt_binary64_1837` `exp-sqrt_binary64_1836` `div-exp_binary64_1834` `rec-exp_binary64_1833` `exp-neg_binary64_1830` `e-exp-1_binary64_1828` `exp-0_binary64_1825` `rem-log-exp_binary64_1824` `rem-exp-log_binary64_1823` `cube-div_binary64_1812` `cube-neg_binary64_1810` `rem-3cbrt-rft_binary64_1809` `rem-3cbrt-lft_binary64_1808` `sqr-neg_binary64_1797` `div-sub_binary64_1788` `mul-1-neg_binary64_1775` `remove-double-neg_binary64_1771` `--rgt-identity_binary64_1769` `+-lft-identity_binary64_1767` `mul0-rgt_binary64_1766` `mul0-lft_binary64_1765` `div0_binary64_1764` `*-inverses_binary64_1763` `+-inverses_binary64_1762` `lft-mult-inverse_binary64_1761` `rgt-mult-inverse_binary64_1760` `remove-double-div_binary64_1759` `difference-of-sqr--1_binary64_1754` `difference-of-sqr-1_binary64_1753` `cancel-sign-sub_binary64_1748` `distribute-neg-frac_binary64_1747` `distribute-frac-neg_binary64_1746` `distribute-neg-out_binary64_1745` `distribute-rgt1-in_binary64_1739` `distribute-lft1-in_binary64_1738` `associate--r-_binary64_1722`

Counts

132 → 148

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	228	3766
1	471	3502
2	1630	3400
3	3187	3400
4	4728	3386
5	4994	3386
6	4935	3386

prune429.0ms (2.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	148	3	151

Error

Counts

151 → 3

Compiler

Compiled 7314 to 5091 computations (30.4% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
0.2b	(.f64 2/3 (.f64 x x))
0.3b	(.f64 (sqrt.f64 (/.f64 1 PI.f64)) (sqrt.f64 (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2))))))
0.3b	(.f64 (sqrt.f64 (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (.f64 (fabs.f64 x) 2))))) (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (sqrt.f64 (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (*.f64 x x)) 2)))))))

rewrite874.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

47×	`add-sqr-sqrt_binary64_1805`
40×	`sqrt-div_binary64_1800`
29×	`sqrt-prod_binary64_1799`
28×	`associate-l_binary64_1724`
23×	`*-un-lft-identity_binary64_1783`
21×	`pow1_binary64_1844` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818`
20×	`associate-r_binary64_1723`
18×	`add-cbrt-cube_binary64_1819` `frac-times_binary64_1793`
14×	`flip3-+_binary64_1786` `flip-+_binary64_1757`
13×	`pow-prod-down_binary64_1854` `associate-*r/_binary64_1725` `unswap-sqr_binary64_1751` `times-frac_binary64_1789`
10×	`prod-exp_binary64_1832`
8×	`cbrt-unprod_binary64_1816`
6×	`associate-*l/_binary64_1726`
5×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801`
4×	`add-log-exp_binary64_1822` `*-commutative_binary64_1714` `unpow-prod-down_binary64_1862` `cube-prod_binary64_1811`
3×	`sqrt-unprod_binary64_1803`
2×	`sqr-pow_binary64_1755`
1×	`div-inv_binary64_1780` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `unpow3_binary64_1849` `cube-mult_binary64_1813`

Counts

4 → 140

Calls

4 calls:

37.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (.f64 (fabs.f64 x) 2))))) (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (sqrt.f64 (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (*.f64 x x)) 2)))))))
23.0ms	(.f64 (sqrt.f64 (/.f64 1 PI.f64)) (sqrt.f64 (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2))))))
7.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
7.0ms	(.f64 2/3 (.f64 x x))

Compiler

Compiled 11858 to 8188 computations (30.9% saved)

series3.4s (16.4%)

Error

Counts

4 → 22

Calls

4 calls:

2.7s	(.f64 (sqrt.f64 (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (.f64 (fabs.f64 x) 2))))) (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (sqrt.f64 (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (*.f64 x x)) 2)))))))
394.0ms	(.f64 (sqrt.f64 (/.f64 1 PI.f64)) (sqrt.f64 (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2))))))
58.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
39.0ms	(.f64 2/3 (.f64 x x))

Compiler

Compiled 11196 to 8142 computations (27.3% saved)

simplify315.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

694×	`associate-r_binary64_1723`
565×	`associate-l_binary64_1724`
451×	`times-frac_binary64_1789`
208×	`associate-+r+_binary64_1715`
207×	`*-commutative_binary64_1714`
136×	`associate-+l+_binary64_1716`
129×	`distribute-rgt-in_binary64_1733`
123×	`distribute-lft-in_binary64_1732`
73×	`associate-/r*_binary64_1727`
69×	`+-commutative_binary64_1713`
63×	`sqr-pow_binary64_1755`
60×	`log-prod_binary64_1869` `associate-*r/_binary64_1725`
55×	`exp-prod_binary64_1835`
52×	`unswap-sqr_binary64_1751`
48×	`cube-prod_binary64_1811`
42×	`associate--r+_binary64_1719`
41×	`associate-*l/_binary64_1726`
40×	`cancel-sign-sub-inv_binary64_1749`
37×	`associate-/l*_binary64_1728`
34×	`associate--l+_binary64_1720`
31×	`distribute-neg-in_binary64_1744`
27×	`sub-neg_binary64_1776`
26×	`distribute-rgt-neg-in_binary64_1741`
20×	`distribute-lft-neg-in_binary64_1740`
19×	`cube-unmult_binary64_1820`
18×	`neg-sub0_binary64_1778`
17×	`swap-sqr_binary64_1750`
16×	`neg-mul-1_binary64_1779`
12×	`unpow3_binary64_1849`
11×	`pow-plus_binary64_1846` `*-rgt-identity_binary64_1773`
10×	`cube-mult_binary64_1813`
9×	`distribute-rgt-out_binary64_1736`
8×	`log-pow_binary64_1872` `rem-square-sqrt_binary64_1795`
7×	`rem-sqrt-square_binary64_1796` `*-lft-identity_binary64_1772`
4×	`distribute-lft-neg-out_binary64_1742`
3×	`mul-1-neg_binary64_1775` `pow-sqr_binary64_1756`
2×	`unpow2_binary64_1848` `unpow1/2_binary64_1847` `unpow1_binary64_1841` `unsub-neg_binary64_1777` `difference-of-squares_binary64_1752` `distribute-rgt-out--_binary64_1737` `associate-/r/_binary64_1729` `associate-+l-_binary64_1718` `associate-+r-_binary64_1717`
1×	`1-exp_binary64_1827` `exp-1-e_binary64_1826` `rem-cbrt-cube_binary64_1807` `rem-cube-cbrt_binary64_1806` `sqr-abs_binary64_1798` `distribute-lft-out_binary64_1734` `count-2_binary64_1731`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_2046` `erf-erfc_binary64_2045` `erf-odd_binary64_2044` `if-if-and-not_binary64_2043` `if-if-and_binary64_2042` `if-if-or-not_binary64_2041` `if-if-or_binary64_2040` `if-not_binary64_2039` `if-same_binary64_2038` `if-false_binary64_2037` `if-true_binary64_2036` `not-gte_binary64_2035` `not-lte_binary64_2034` `not-gt_binary64_2033` `not-lt_binary64_2032` `gte-same_binary64_2031` `lte-same_binary64_2030` `gt-same_binary64_2029` `lt-same_binary64_2028` `sinh---cosh_binary64_1975` `sinh-+-cosh_binary64_1974` `sinh-cosh_binary64_1973` `tanh-def-c_binary64_1972` `tanh-def-b_binary64_1971` `tanh-def-a_binary64_1970` `cosh-def_binary64_1969` `sinh-def_binary64_1968` `tan-neg_binary64_1915` `cos-neg_binary64_1914` `sin-neg_binary64_1913` `tan-0_binary64_1912` `cos-0_binary64_1911` `sin-0_binary64_1910` `hang-m-tan_binary64_1909` `hang-p-tan_binary64_1908` `hang-m0-tan_binary64_1907` `hang-p0-tan_binary64_1906` `hang-0m-tan_binary64_1905` `hang-0p-tan_binary64_1904` `tan-+PI/2_binary64_1903` `tan-+PI_binary64_1902` `tan-PI_binary64_1901` `tan-PI/3_binary64_1900` `tan-PI/4_binary64_1899` `tan-PI/6_binary64_1898` `cos-+PI/2_binary64_1897` `cos-+PI_binary64_1896` `cos-PI_binary64_1895` `cos-PI/2_binary64_1894` `cos-PI/3_binary64_1893` `cos-PI/4_binary64_1892` `cos-PI/6_binary64_1891` `sin-+PI/2_binary64_1890` `sin-+PI_binary64_1889` `sin-PI_binary64_1888` `sin-PI/2_binary64_1887` `sin-PI/3_binary64_1886` `sin-PI/4_binary64_1885` `sin-PI/6_binary64_1884` `sub-1-sin_binary64_1883` `sub-1-cos_binary64_1882` `-1-add-sin_binary64_1881` `-1-add-cos_binary64_1880` `1-sub-sin_binary64_1879` `1-sub-cos_binary64_1878` `cos-sin-sum_binary64_1877` `log-E_binary64_1873` `log-rec_binary64_1871` `log-div_binary64_1870` `pow-base-0_binary64_1867` `unpow1/3_binary64_1850` `exp-to-pow_binary64_1845` `pow-base-1_binary64_1843` `unpow0_binary64_1842` `unpow-1_binary64_1840` `exp-lft-cube_binary64_1839` `exp-lft-sqr_binary64_1838` `exp-cbrt_binary64_1837` `exp-sqrt_binary64_1836` `div-exp_binary64_1834` `rec-exp_binary64_1833` `prod-exp_binary64_1832` `exp-diff_binary64_1831` `exp-neg_binary64_1830` `exp-sum_binary64_1829` `e-exp-1_binary64_1828` `exp-0_binary64_1825` `rem-log-exp_binary64_1824` `rem-exp-log_binary64_1823` `cube-div_binary64_1812` `cube-neg_binary64_1810` `rem-3cbrt-rft_binary64_1809` `rem-3cbrt-lft_binary64_1808` `sqr-neg_binary64_1797` `div-sub_binary64_1788` `/-rgt-identity_binary64_1774` `remove-double-neg_binary64_1771` `sub0-neg_binary64_1770` `--rgt-identity_binary64_1769` `+-rgt-identity_binary64_1768` `+-lft-identity_binary64_1767` `mul0-rgt_binary64_1766` `mul0-lft_binary64_1765` `div0_binary64_1764` `*-inverses_binary64_1763` `+-inverses_binary64_1762` `lft-mult-inverse_binary64_1761` `rgt-mult-inverse_binary64_1760` `remove-double-div_binary64_1759` `difference-of-sqr--1_binary64_1754` `difference-of-sqr-1_binary64_1753` `cancel-sign-sub_binary64_1748` `distribute-neg-frac_binary64_1747` `distribute-frac-neg_binary64_1746` `distribute-neg-out_binary64_1745` `distribute-rgt-neg-out_binary64_1743` `distribute-rgt1-in_binary64_1739` `distribute-lft1-in_binary64_1738` `distribute-lft-out--_binary64_1735` `associate-/l/_binary64_1730` `associate--r-_binary64_1722` `associate--l-_binary64_1721`

Counts

162 → 376

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	530	14877
1	1342	13216
2	4643	12547
3	5355	12547

prune4.9s (23.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	376	0	376
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	376	3	379

Error

Counts

379 → 3

Compiler

Compiled 44509 to 30492 computations (31.5% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
0.2b	(.f64 2/3 (.f64 x x))
0.3b	(/.f64 (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (*.f64 x x)) 2)))) (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)

rewrite249.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

31×	`add-sqr-sqrt_binary64_1805`
24×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
18×	`times-frac_binary64_1789`
16×	`add-exp-log_binary64_1821`
15×	`sqrt-prod_binary64_1799`
13×	`add-cbrt-cube_binary64_1819`
10×	`pow1_binary64_1844`
8×	`associate-r_binary64_1723`
6×	`associate-/r_binary64_1727` `prod-exp_binary64_1832` `associate-l*_binary64_1724`
4×	`add-log-exp_binary64_1822` `cbrt-unprod_binary64_1816` `unswap-sqr_binary64_1751` `unpow-prod-down_binary64_1862`
3×	`associate-/l*_binary64_1728` `pow-prod-down_binary64_1854`
2×	`associate-/l/_binary64_1730` `*-commutative_binary64_1714` `sqr-pow_binary64_1755`
1×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `div-exp_binary64_1834` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `div-inv_binary64_1780` `flip3-+_binary64_1786` `flip-+_binary64_1757` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`

Counts

4 → 98

Calls

4 calls:

13.0ms	(/.f64 (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (*.f64 x x)) 2)))) (sqrt.f64 PI.f64))
9.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
6.0ms	(.f64 2/3 (.f64 x x))
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 4117 to 2554 computations (38% saved)

series481.0ms (2.3%)

Error

Counts

4 → 12

Calls

4 calls:

356.0ms	(/.f64 (+.f64 (.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (*.f64 x x)) 2)))) (sqrt.f64 PI.f64))
72.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
33.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1040 to 799 computations (23.2% saved)

simplify142.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

705×	`associate-l_binary64_1724`
593×	`associate-r_binary64_1723`
376×	`distribute-rgt-in_binary64_1733`
353×	`distribute-lft-in_binary64_1732`
149×	`times-frac_binary64_1789`
110×	`associate-+l+_binary64_1716`
108×	`associate-+r+_binary64_1715`
104×	`cancel-sign-sub-inv_binary64_1749`
85×	`*-commutative_binary64_1714`
60×	`associate-*l/_binary64_1726`
55×	`associate-/l*_binary64_1728`
51×	`associate-/l/_binary64_1730`
50×	`associate-*r/_binary64_1725`
48×	`exp-prod_binary64_1835`
47×	`log-prod_binary64_1869`
41×	`distribute-rgt-neg-in_binary64_1741`
40×	`cube-prod_binary64_1811`
37×	`distribute-lft-neg-in_binary64_1740` `associate-/r*_binary64_1727` `associate--r+_binary64_1719`
31×	`sqr-pow_binary64_1755`
30×	`+-commutative_binary64_1713`
29×	`associate--l+_binary64_1720`
27×	`sub-neg_binary64_1776`
26×	`distribute-neg-in_binary64_1744`
24×	`unswap-sqr_binary64_1751`
21×	`associate-/r/_binary64_1729`
20×	`distribute-rgt-out_binary64_1736`
19×	`cube-unmult_binary64_1820`
16×	`neg-mul-1_binary64_1779` `neg-sub0_binary64_1778`
15×	`swap-sqr_binary64_1750`
10×	`associate-+l-_binary64_1718` `associate-+r-_binary64_1717`
9×	`pow-plus_binary64_1846`
8×	`distribute-lft-neg-out_binary64_1742`
6×	`log-pow_binary64_1872` `unsub-neg_binary64_1777` `*-rgt-identity_binary64_1773` `pow-sqr_binary64_1756` `distribute-rgt-out--_binary64_1737`
5×	`distribute-lft-out_binary64_1734`
4×	`unpow3_binary64_1849` `rem-sqrt-square_binary64_1796` `/-rgt-identity_binary64_1774` `distribute-rgt-neg-out_binary64_1743`
3×	`log-div_binary64_1870` `div-sub_binary64_1788` `associate--l-_binary64_1721`
2×	`count-2_binary64_1731`
1×	`unpow1/3_binary64_1850` `unpow2_binary64_1848` `unpow1/2_binary64_1847` `unpow1_binary64_1841` `1-exp_binary64_1827` `cube-mult_binary64_1813` `cube-div_binary64_1812` `sqr-abs_binary64_1798` `rem-square-sqrt_binary64_1795` `*-lft-identity_binary64_1772` `distribute-neg-frac_binary64_1747` `distribute-lft-out--_binary64_1735`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_2046` `erf-erfc_binary64_2045` `erf-odd_binary64_2044` `if-if-and-not_binary64_2043` `if-if-and_binary64_2042` `if-if-or-not_binary64_2041` `if-if-or_binary64_2040` `if-not_binary64_2039` `if-same_binary64_2038` `if-false_binary64_2037` `if-true_binary64_2036` `not-gte_binary64_2035` `not-lte_binary64_2034` `not-gt_binary64_2033` `not-lt_binary64_2032` `gte-same_binary64_2031` `lte-same_binary64_2030` `gt-same_binary64_2029` `lt-same_binary64_2028` `sinh---cosh_binary64_1975` `sinh-+-cosh_binary64_1974` `sinh-cosh_binary64_1973` `tanh-def-c_binary64_1972` `tanh-def-b_binary64_1971` `tanh-def-a_binary64_1970` `cosh-def_binary64_1969` `sinh-def_binary64_1968` `tan-neg_binary64_1915` `cos-neg_binary64_1914` `sin-neg_binary64_1913` `tan-0_binary64_1912` `cos-0_binary64_1911` `sin-0_binary64_1910` `hang-m-tan_binary64_1909` `hang-p-tan_binary64_1908` `hang-m0-tan_binary64_1907` `hang-p0-tan_binary64_1906` `hang-0m-tan_binary64_1905` `hang-0p-tan_binary64_1904` `tan-+PI/2_binary64_1903` `tan-+PI_binary64_1902` `tan-PI_binary64_1901` `tan-PI/3_binary64_1900` `tan-PI/4_binary64_1899` `tan-PI/6_binary64_1898` `cos-+PI/2_binary64_1897` `cos-+PI_binary64_1896` `cos-PI_binary64_1895` `cos-PI/2_binary64_1894` `cos-PI/3_binary64_1893` `cos-PI/4_binary64_1892` `cos-PI/6_binary64_1891` `sin-+PI/2_binary64_1890` `sin-+PI_binary64_1889` `sin-PI_binary64_1888` `sin-PI/2_binary64_1887` `sin-PI/3_binary64_1886` `sin-PI/4_binary64_1885` `sin-PI/6_binary64_1884` `sub-1-sin_binary64_1883` `sub-1-cos_binary64_1882` `-1-add-sin_binary64_1881` `-1-add-cos_binary64_1880` `1-sub-sin_binary64_1879` `1-sub-cos_binary64_1878` `cos-sin-sum_binary64_1877` `log-E_binary64_1873` `log-rec_binary64_1871` `pow-base-0_binary64_1867` `exp-to-pow_binary64_1845` `pow-base-1_binary64_1843` `unpow0_binary64_1842` `unpow-1_binary64_1840` `exp-lft-cube_binary64_1839` `exp-lft-sqr_binary64_1838` `exp-cbrt_binary64_1837` `exp-sqrt_binary64_1836` `div-exp_binary64_1834` `rec-exp_binary64_1833` `prod-exp_binary64_1832` `exp-diff_binary64_1831` `exp-neg_binary64_1830` `exp-sum_binary64_1829` `e-exp-1_binary64_1828` `exp-1-e_binary64_1826` `exp-0_binary64_1825` `rem-log-exp_binary64_1824` `rem-exp-log_binary64_1823` `cube-neg_binary64_1810` `rem-3cbrt-rft_binary64_1809` `rem-3cbrt-lft_binary64_1808` `rem-cbrt-cube_binary64_1807` `rem-cube-cbrt_binary64_1806` `sqr-neg_binary64_1797` `mul-1-neg_binary64_1775` `remove-double-neg_binary64_1771` `sub0-neg_binary64_1770` `--rgt-identity_binary64_1769` `+-rgt-identity_binary64_1768` `+-lft-identity_binary64_1767` `mul0-rgt_binary64_1766` `mul0-lft_binary64_1765` `div0_binary64_1764` `*-inverses_binary64_1763` `+-inverses_binary64_1762` `lft-mult-inverse_binary64_1761` `rgt-mult-inverse_binary64_1760` `remove-double-div_binary64_1759` `difference-of-sqr--1_binary64_1754` `difference-of-sqr-1_binary64_1753` `difference-of-squares_binary64_1752` `cancel-sign-sub_binary64_1748` `distribute-frac-neg_binary64_1746` `distribute-neg-out_binary64_1745` `distribute-rgt1-in_binary64_1739` `distribute-lft1-in_binary64_1738` `associate--r-_binary64_1722`

Counts

110 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	188	3889
1	414	3652
2	1151	3574
3	4678	3574
4	4996	3574

prune327.0ms (1.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	126	3	129

Error

Counts

129 → 3

Compiler

Compiled 6077 to 3787 computations (37.7% saved)

regimes954.0ms (4.6%)

Accuracy

Total 0.1b remaining (99.8%)

Threshold costs 0.1b (99.8%)

Compiler

Compiled 19040 to 10643 computations (44.1% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64_1714`
3×	`+-commutative_binary64_1713`
1×	`1-exp_binary64_1827`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `if-if-and-not_binary64_2043` `if-if-and_binary64_2042` `if-if-or-not_binary64_2041` `if-if-or_binary64_2040` `if-not_binary64_2039` `if-same_binary64_2038` `if-false_binary64_2037` `if-true_binary64_2036` `tan-0_binary64_1912` `cos-0_binary64_1911` `sin-0_binary64_1910` `unpow1_binary64_1841` `e-exp-1_binary64_1828` `exp-1-e_binary64_1826` `exp-0_binary64_1825` `sqr-abs_binary64_1798` `sqr-neg_binary64_1797` `neg-mul-1_binary64_1779` `neg-sub0_binary64_1778` `unsub-neg_binary64_1777` `sub-neg_binary64_1776` `mul-1-neg_binary64_1775` `/-rgt-identity_binary64_1774` `-rgt-identity_binary64_1773` `-lft-identity_binary64_1772` `remove-double-neg_binary64_1771` `sub0-neg_binary64_1770` `--rgt-identity_binary64_1769` `+-rgt-identity_binary64_1768` `+-lft-identity_binary64_1767` `cancel-sign-sub-inv_binary64_1749` `cancel-sign-sub_binary64_1748` `distribute-neg-frac_binary64_1747` `distribute-frac-neg_binary64_1746` `distribute-neg-out_binary64_1745` `distribute-neg-in_binary64_1744` `distribute-rgt-neg-out_binary64_1743` `distribute-lft-neg-out_binary64_1742` `distribute-rgt-neg-in_binary64_1741` `distribute-lft-neg-in_binary64_1740`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	50
1	36	50
2	35	50

end0.0ms (0%)

sample3.1s (14.8%)

Algorithm

1×

intervals

Results

777.0ms	8000×	body	128	valid
104.0ms	8002×	pre	128	true
0.0ms	2×	body	128	invalid

Compiler

Compiled 3591 to 2056 computations (42.7% saved)

Details

analyze11.0ms (0.1%)

sample45.0ms (0.2%)

simplify215.0ms (1%)

prune21.0ms (0.1%)

localize27.0ms (0.1%)

rewrite581.0ms (2.8%)

series411.0ms (2%)

simplify242.0ms (1.2%)

prune3.0s (14.3%)

localize20.0ms (0.1%)

rewrite356.0ms (1.7%)

series500.0ms (2.4%)

simplify203.0ms (1%)

prune429.0ms (2.1%)

localize31.0ms (0.2%)

rewrite874.0ms (4.2%)

series3.4s (16.4%)

simplify315.0ms (1.5%)

prune4.9s (23.4%)

localize19.0ms (0.1%)

rewrite249.0ms (1.2%)

series481.0ms (2.3%)

simplify142.0ms (0.7%)

prune327.0ms (1.6%)

regimes954.0ms (4.6%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.1s (14.8%)

Profiling